Skip to main content
Springer Nature Link
Log in

Axiomatic data type specifications: A first order theory of linear lists

  • Published:
Acta Informatica Aims and scope Submit manuscript

Summary

A formal first order theory is given as a specification of the data type of linear lists. Various aspects and properties of the theory are explored, such as consistency, completeness and independence. In addition, implementation issues and their relation to the formal theory are also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. deBakker, J.W., Meertens, L.G.L.T.: On the completeness of the inductive assertion method. J. Comput. System Sci. 11, 323–357 (1975)

    Google Scholar 

  2. Cartwright, R. Jr.: A practical formal semantic definition and verification system for TYPED LISP. Stanford Artificial Intelligence Laboratory Memo AIM-296, December 1976

  3. Chang, C.C., Keisler, H.J.: Model theory. Studies in logic and the foundations of mathematics. (A. Heyting, ed.) Vol. 73, Amsterdam: North-Holland, 1973

    Google Scholar 

  4. Enderton, H.B.: A mathematical introduction to logic. New York: Academic Press, 1972

    Google Scholar 

  5. Floyd, R.W.: Assigning meaning to programs. In: Mathematical aspects of computer science, (J. Schwartz, ed.) Vol. 19, Providence, R.I.: American Mathematical Society 1976

    Google Scholar 

  6. Guttag, J.V., Horowitz, E., Musser, D.R.: Some extensions to algebraic specifications. Information Sciences Institute Report RR-76-50, Marina del Rey, California 1976

  7. Guttag, J.V.: Abstract data types and the development of data structures. Communications of the ACM, Vol.20, 396–404 (1977)

    Google Scholar 

  8. Hoare, C.A.R.: An axiomatic basis for computer programming. Communications of the ACM 12, 576–580 (1969)

    Google Scholar 

  9. Hoare, C.A.R.: Procedures and parameters: An axiomatic approach. (E. Engeler ed.) Lecture Notes in Mathematics, Vol. 188, Berlin-Heidelberg-New York: Springer 1971

    Google Scholar 

  10. Hoare, C.A.R.: Notes on data structuring. In: Structured programming. New York: Academic Press 1972

    Google Scholar 

  11. Kleene, S.C.: Introduction to metamathematics. Amsterdam: North-Holland 1952

    Google Scholar 

  12. Kleene, S.C.: Mathematical logic. New York: John Wiley 1967

    Google Scholar 

  13. Liskov, B., Zilles, S.: An introduction to formal specifications of data abstractions. In: Current trends in programming methodology, Vol. 1 (R.T. Yeh, ed.), Englewood Cliffs, N.J.: Prentice-Hall, 1977

    Google Scholar 

  14. Manna, Z.: The correctness of programs. J. Comput. System Sci. 3, 119–127 (1969)

    Google Scholar 

  15. Mendelson, E.: Introduction to mathematical logic. New York: Van Nostrand 1964

    Google Scholar 

  16. Oppen, D.C.: Reasoning about recursively defined data structures. Proc. 5th ACM symposium on principles of programming languages, Tucson, 151–157. New York: ACM 1978

    Google Scholar 

  17. Soni, D., Moore, D.: The theory of linear lists with head and tail admits elimination of quantifiers. Computer and Information Science Department, The Ohio State University, Technical Report, 1979

  18. Wegbreit, B., Morris, J.H., Jr.:Subgoal induction. Communications of the ACM, 20, 209–222 (1977)

    Google Scholar 

  19. Yeh, R.T., (ed.): Current trends in programming methodology, Vol. 4: Data structuring. Englewood Cliffs, N.J.: Prentice-Hall, 1978

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer and Information Science, The Ohio State University, 43210, Columbus, Ohio, USA

    Daniel J. Moore

  2. Computer Science Department, SUNY at Stony Brook, New York, USA

    Bruce Russell

Authors
  1. Daniel J. Moore
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Bruce Russell
    View author publications

    You can also search for this author inPubMed Google Scholar

Additional information

Now at: Bell Laboratories, 600 Mountain Ave., Room 5E-116, Murray Hill, New Jersey 07974, USA

Now at: TSI International, 50 Washington St., Norwalk, Connecticut 06854, USA

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moore, D.J., Russell, B. Axiomatic data type specifications: A first order theory of linear lists. Acta Informatica 15, 193–207 (1981). https://doi.org/10.1007/BF00289260

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00289260

Keywords